The Nature of Algebra Through Observational Logic
According to the Merriam-Webster dictionary (2013), mathematics defined is “the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformation, and generalizations.” One of the principal reasons for studying mathematics is learning to solve problems and think critically. Such is the case for the numbers game, Guess Your Card, which requires you to figure out what numbers are on the cards you have picked.
While playing with three other players, I can see that Andy has the cards one, five, and seven. Belle has the cards five, four, and seven and Carol has the cards two, four, and six.
Andy: 1,5,7
Belle: 5,4,7
Carol: 2,4,6 Andy draws the question card, “Do you see two or more players whose cards sum to the same value and he answers “yes.” Given the information, I can see that the sum of Belle’s cards equals 16 and the sum of Carol’s cards equals 12. These are two different sums, but Andy said he sees at least two players who cards have the same sum. This tells me that my cards must add up to either a 16 or a 12.
(Sum of Belle’s cards: 5+4+7=16)
(Sum of Carol’s cards: 2+4+6=12) Next Belle draws the question card, “Of the five odd numbers, how many different odd numbers do you see?” She answers, “All of them.” From this information, Andy is able to figure out that he has a one, a five, and a seven.
I know that the only cards that Belle sees from Andy and Carol that are odd are one, five, and seven. This means that I must have a three and a nine. As mentioned before, I also know that the sum of my cards is either a 16 or and12. The sum of three plus nine equals 12, however, the smallest card is one and when added it will make my sum 13. The easiest way to find the number of my third card is subtracting 16 from 12, or 16-9-3, which gives me 4. My cards are a four, a three, and a nine.
Me: 4,3,9
To solve this problem, I simply used
While playing with three other players, I can see that Andy has the cards one, five, and seven. Belle has the cards five, four, and seven and Carol has the cards two, four, and six.
Andy: 1,5,7
Belle: 5,4,7
Carol: 2,4,6 Andy draws the question card, “Do you see two or more players whose cards sum to the same value and he answers “yes.” Given the information, I can see that the sum of Belle’s cards equals 16 and the sum of Carol’s cards equals 12. These are two different sums, but Andy said he sees at least two players who cards have the same sum. This tells me that my cards must add up to either a 16 or a 12.
(Sum of Belle’s cards: 5+4+7=16)
(Sum of Carol’s cards: 2+4+6=12) Next Belle draws the question card, “Of the five odd numbers, how many different odd numbers do you see?” She answers, “All of them.” From this information, Andy is able to figure out that he has a one, a five, and a seven.
I know that the only cards that Belle sees from Andy and Carol that are odd are one, five, and seven. This means that I must have a three and a nine. As mentioned before, I also know that the sum of my cards is either a 16 or and12. The sum of three plus nine equals 12, however, the smallest card is one and when added it will make my sum 13. The easiest way to find the number of my third card is subtracting 16 from 12, or 16-9-3, which gives me 4. My cards are a four, a three, and a nine.
Me: 4,3,9
To solve this problem, I simply used
References: Mathematics. 2013. In Merriam-Webster.com. Retrieved July 16, 2013, from http://www.merriam-webster.com/dictionary/mathematics